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the Hadamard Theorem says that any simply connected, complete Riemannian manifold of non-positive sectional curvature is diffeomorphic to $R_{n}$. I know this is a stupid question, but what am I missing here?

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    $\begingroup$ Hyperbolic space is diffeomorphic to $\mathbb{R}^n$. $\endgroup$ – Max Oct 30 '18 at 15:53
  • $\begingroup$ So that's how it is..I am learning differential geometry by myself, the textbook never mention that. Thanks. $\endgroup$ – knot Oct 30 '18 at 15:58

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